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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="measure1.html#M3" title="MEASURE1:mode.3">sigma_Measure</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>, <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> ;<br/>







<b>assume </b><a NAME="E1:94"/>
<font color="Maroon" title="c4">f</font> <a href="mesfunc6.html#R3" title="MESFUNC6:pred.3">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 ;<br/>

<a NAME="E2:94"/><b>then </b>
 <a href="mesfunc5.html#K1" title="MESFUNC5:func.1">R_EAL</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Maroon" title="c3">M</font>
 
<b>by </b><i><a class="ref" href="mesfunc6.html#D9" target="_self" title="MESFUNC6:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E3:94"/>
(  <a href="supinf_1.html#K2" title="SUPINF_1:func.2">-infty</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font> &amp;  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c4">f</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  )
 <b>by </b><i><a class="ref" href="mesfunc5.html#T102" title="MESFUNC5:th.102">MESFUNC5:102</a></i>;<br/>


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